二阶椭圆问题的Q_2-Q_1混合元格式

Q2-Q1 Mixed Finite Element Scheme for Second Order Elliptic Problem

利用格林公式将二阶椭圆问题转化为一个与其等价的新的混合变分形式,基于此新的混合变分形式,给出了满足Falk-Osborn理论的Q2-Q1格式,该格式避开了传统变分形式中双线性型不满足强椭圆性的弱点,在特殊矩形剖分下通过定义插值算子,在不需要满足离散的LBB条件下,利用一些新技巧和有限元插值理论得到了L2模和能量模的最优误差估计.

In this paper, the new equivalent mixed variational form for second order elliptic problem was presented by using Green formula. Based on the mixed variational form for second order elliptic problem, The paper built Q2-Q1 scheme contented Falk - Osborn theory. The scheme to avoid the traditional form of variational bilinear form does not satisfy strong elliptic vulnerabitities. Under the special rectangular subdivision, the interpolation operator was defined. Then by using finite element interpolation theory and some new techniques, the error estimates of optimal order were derived both in the energ norm and L2-norm without using the discrete LBB conditions.